11 votes

What is a particle in the context of QFT with interactions?

In quantum field theory (QFT) the notion of a field is fundamental, not the notion of a particle. You can search for local excitations of the fields and identify these with particles, but this can ...
Carlo Beenakker's user avatar
6 votes

Are these two representations of $SU(2)$ equivalent?

It suffices to look at the action of $\mathrm{diag}(t,t^{-1})\in\mathrm{SU}_2$ where $|t|=1$. On $\mathrm{Sym}^{n-1}(\mathbb C^2)$ it acts with eigenvalue $t^{1-n},t^{3-n},\dots,t^{n-1}$, and thus the ...
Kenta Suzuki's user avatar
  • 1,282
4 votes

Homology of symplectic groups in the unstable range

The optimal stabilization range for third homology of the symplectic groups has been determined by Marco Schlichting and Husney Parvez Sarwar in https://arxiv.org/abs/2111.01539. Their result states ...
Matthias Wendt's user avatar
3 votes

Example of a finite group $G$ with low dimensional cohomology not generated by Stiefel-Whitney classes of flat vector bundles over $BG$

I recently wondered about this question myself. For anyone else who might have wondered about this, I'm going to share my findings. First, I would like to note that the paper of Gunarwardena, Kahn and ...
Matthias Wendt's user avatar
3 votes

Irreducibility of Gelfand-Serganova strata

Here is an explicit example. There are examples of realization spaces of matroids (which are, up to a torus quotient, Gelfand-Serganova strata in the Grassmannian) which are disconnected. I believe ...
Matt Larson's user avatar
1 vote

Determine monodromy representation from local system

In general, I would say that there is no way around the fact that the answer uses the fact that a sheaf on $[0,1]$ is constant. Does this help? Instead of the pushforward of the constant sheaf $k$ of ...
Tom Goodwillie's user avatar

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